A Model Structure on the Category of Topological Categories

Abstract

In this article, we construct a cofibrantly generated Quillen model structure on the category of small topological categories ${\mathbf{Cat}}_{\mathbf{Top}}$. It is Quillen equivalent to the Joyal model structure of $(\infty ,1)$-categories and the Bergner model structure on ${\mathbf{Cat}}_{\mathbf{sSet}}$.

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